State-of-the-art in the proposed field of research and survey of the relevant literature
========================================================================================

In the context of soc fuel cells, building first principle models
requires very precise knowledge about the soc microstructure, its
porosity, electrode thickness, structure of the individual layers, and
other factors (Zou, Manzie, and Nesic 2015). Models range from very
simple calculations of the specific reactions, without detailed
consideration of the cell microstructure and kinetics (Badur et al.
2018), detailed information on mass transport, heterogeneous chemistry
and porous media transport (Kupecki et al. 2018) all the way to very
detailed 2D-models for reversibly operated and industrial scale solid
oxide cells (Subotić et al. 2020).

Various fault modes have profound influence on the behaviour of soc
systems too. Typical cases include carbon depositions, sulphur
poisoning, or nickel reoxidation on the anode side (Moçoteguy and Brisse
2013). These mechanisms can bring about the irreversible deterioration
of the cell’s electrochemical and micro-structural performance, thus
significantly shortening its life-time.

For accurate implementation of the above listed approaches, accelerated
and long term testing is usually needed. Such experiments allow very
detailed chemical and electrochemical characterisations of soc systems.
However, experimental investigations are time-consuming and expensive.
There are very few published results in the field of soc. Researchers
from FZ JĂźlich as one of the pioneers in the field of sofc among the
first performed almost a decade long experiment (Blum et al. 2016).
Similar results but more detailed analysis on almost 30,000 hours long
experiment are also available (Menzler, Sebold, and Guillon 2017). In
the area of soec, the available results are even scarcer (Yan et al.
2017; Tietz et al. 2012)

In the above results, the characterisation of soc systems was almost
exclusively done by fairly straightforward approaches such as
polarisation curves, eis or drt. There have been only a limited number
of cases addressing the actual non-linear nature of these
systems (Subotić et al. 2021, 2020) A logical continuation is the
application of various data-driven techniques in order to characterise
and predict the performance of soc systems. An overview of the published
results in the field of soc systems is shown in Table `1 <#tab:soa>`__.
It is clear that electrolyses, i.e. soecs and dual-mode (reversible soc)
systems are underrepresented.

.. container::
   :name: tab:soa

   .. table:: List of publications of data-driven approaches for various
   soc systems

      +-------------+-------------+-------------+-------------+-------------+
      |             | SOEC        | SOFC        | catalyst    | rSOC        |
      +=============+=============+=============+=============+=============+
      | control     |             | (Jurado     |             |             |
      |             |             | 2003; X.-J. |             |             |
      |             |             | Wu et al.   |             |             |
      |             |             | 2007; Huo   |             |             |
      |             |             | et al.      |             |             |
      |             |             | 2008;       |             |             |
      |             |             | Hajimolana  |             |             |
      |             |             | et al.      |             |             |
      |             |             | 2013;       |             |             |
      |             |             | Marchetti   |             |             |
      |             |             | et al.      |             |             |
      |             |             | 2011) S     |             |             |
      +-------------+-------------+-------------+-------------+-------------+
      | design      |             | (Nassef et  |             |             |
      | parameter   |             | al. 2019;   |             |             |
      | o           |             | Song et al. |             |             |
      | ptimization |             | 2020;       |             |             |
      |             |             | Bozorgmehri |             |             |
      |             |             | and Hamedi  |             |             |
      |             |             | 2012; Yan   |             |             |
      |             |             | et al.      |             |             |
      |             |             | 2019)       |             |             |
      +-------------+-------------+-------------+-------------+-------------+
      | des         |             | (Le,        |             |             |
      | ign/process |             | Nguyen, and |             |             |
      | parameter   |             | Nguyen      |             |             |
      | o           |             | 2019)       |             |             |
      | ptimization |             |             |             |             |
      +-------------+-------------+-------------+-------------+-------------+
      | fault       |             | (Wu and Ye  |             |             |
      | detection   |             | 2016; Zhang |             |             |
      |             |             | et al.      |             |             |
      |             |             | 2018; Pahon |             |             |
      |             |             | et al.      |             |             |
      |             |             | 2016)       |             |             |
      +-------------+-------------+-------------+-------------+-------------+
      | mu          | (Grondin et |             |             |             |
      | lti-physics | al. 2012)   |             |             |             |
      | model       |             |             |             |             |
      | enhancement |             |             |             |             |
      +-------------+-------------+-------------+-------------+-------------+
      | performance |             | (Xu et al.  |             |             |
      | o           |             | 2020) S     |             |             |
      | ptimization |             |             |             |             |
      +-------------+-------------+-------------+-------------+-------------+
      | performance | (Zahadat    | (Arriagada  | (GĂźnay et   |             |
      | prediction  | and         | 2002; Marra | al. 2011)   |             |
      |             | Milewski    | et al.      |             |             |
      |             | 2015; Han   | 2013; X.-j. |             |             |
      |             | et al.      | Wu et al.   |             |             |
      |             | 2019; Zhang | 2007;       |             |             |
      |             | et al.      | Milewski    |             |             |
      |             | 2017)       | and Świrski |             |             |
      |             |             | 2009;       |             |             |
      |             |             | Chaichana   |             |             |
      |             |             | et al.      |             |             |
      |             |             | 2011;       |             |             |
      |             |             | Baldinelli  |             |             |
      |             |             | et al.      |             |             |
      |             |             | 2018;       |             |             |
      |             |             | Chakraborty |             |             |
      |             |             | 2009;       |             |             |
      |             |             | Entchev and |             |             |
      |             |             | Yang 2007;  |             |             |
      |             |             | Sorrentino  |             |             |
      |             |             | et al.      |             |             |
      |             |             | 2014;       |             |             |
      |             |             | Gebregergis |             |             |
      |             |             | et al.      |             |             |
      |             |             | 2008; Chen, |             |             |
      |             |             | Chen, and   |             |             |
      |             |             | Zhang 2019; |             |             |
      |             |             | Song et al. |             |             |
      |             |             | 2021)       |             |             |
      +-------------+-------------+-------------+-------------+-------------+
      | p           |             | (Dolenc et  |             |             |
      | erformance/ |             | al. 2017)   |             |             |
      | degradation |             |             |             |             |
      | prediction  |             |             |             |             |
      +-------------+-------------+-------------+-------------+-------------+
      | process     |             | (Ahn et al. |             | (Salehi and |
      | parameter   |             | 2019) S     |             | Gh          |
      | o           |             |             |             | olaminezhad |
      | ptimisation |             |             |             | 2018)       |
      +-------------+-------------+-------------+-------------+-------------+

[tab:soa]

Preliminary results
-------------------

Members of both teams have a substantial track record in the field of
soc electro-chemical characterisation (KÜnigshofer, Pongratz, et al.
2021; Höber et al. 2021), modelling (Žnidarič et al. 2021) and
performing fault detection of various soc based systems (KÜnigshofer,
BoĹĄkoski, et al. 2021; Nusev et al. 2021). In the last year tug and jsi
teams have carried out preliminary investigations on using various data
driven techniques on soc systems.

tug team members have successfully implemented vanilla deep-neural
networks for modelling soc systems (Mütter 2021; Subotić, Eibl, and
Hochenauer 2021). The results show very good potential to predict sofc
performance by modelling polarisation curves and eis characteristics.

Additionally, the jsi team has addressed the issues of stochastic model
parameters of lumped sofc models (Žnidarič et al. 2021). Using the vb
approach it was shown that the parameters of the resulting lumped model
have indeed stochastic nature. As a result, each frequency point of the
obtained impedance curves is described with its own posterior
distribution that accommodates the underlying uncertainties (both
measurement and system’s). Despite these promising results, the issues
of explainability and more importantly incorporating experts knowledge
are still open issues.

.. container:: references hanging-indent
   :name: refs

   .. container::
      :name: ref-10.1016/j.applthermaleng.2019.114861

      Ahn, Ji Ho, Min Jae Kim, Yeon Woo Cho, and Tong Seop Kim. 2019. “A
      Quadruple Power Generation System for Very High Efficiency and Its
      Performance Optimization Using an Artificial Intelligence Method.”
      *Applied Thermal Engineering* 168: 114861.
      https://doi.org/10.1016/j.applthermaleng.2019.114861.

   .. container::
      :name: ref-10.1016/S0378-7753_02_00314-2

      Arriagada, J. 2002. “Artificial Neural Network Simulator for Sofc
      Performance Prediction.” *Journal of Power Sources* 112 (1):
      54–60. https://doi.org/10.1016/s0378-7753(02)00314-2.

   .. container::
      :name: ref-10.1016/j.energy.2018.05.203

      Badur, Janusz, Marcin Lemański, Tomasz Kowalczyk, Paweł
      Ziółkowski, and Sebastian Kornet. 2018. “Zero-Dimensional Robust
      Model of an SOFC with Internal Reforming for Hybrid Energy
      Cycles.” *Energy* 158: 128–38.
      https://doi.org/10.1016/j.energy.2018.05.203.

   .. container::
      :name: ref-10.3390/app9010051

      Baldinelli, Arianna, Linda Barelli, Gianni Bidini, Fabio Bonucci,
      and Feride Iskenderoğlu. 2018. “Regarding Solid Oxide Fuel Cells
      Simulation Through Artificial Intelligence: A Neural Networks
      Application.” *Applied Sciences* 9 (1): 51.
      https://doi.org/10.3390/app9010051.

   .. container::
      :name: ref-10.1002/ente.201600114

      Blum, Ludger, L. G. J. de Haart, JĂźrgen Malzbender, Nikolaos
      Margaritis, and Norbert H. Menzler. 2016. “Anode-Supported Solid
      Oxide Fuel Cell Achieves 70 000 Hours of Continuous Operation.”
      *Energy Technology* 4 (8): 939–42.
      https://doi.org/10.1002/ente.201600114.

   .. container::
      :name: ref-10.1002/fuce.201100140

      Bozorgmehri, S., and M. Hamedi. 2012. “Modeling and Optimization
      of Anode-Supported Solid Oxide Fuel Cells on Cell Parameters via
      Artificial Neural Network and Genetic Algorithm.” *Fuel Cells* 12
      (1): 11–23. https://doi.org/10.1002/fuce.201100140.

   .. container::
      :name: ref-10.1016/j.ijhydene.2011.10.051

      Chaichana, Kattiyapon, Yaneeporn Patcharavorachot, Bhawasut
      Chutichai, Dang Saebea, Suttichai Assabumrungrat, and Amornchai
      Arpornwichanop. 2011. “Neural Network Hybrid Model of a Direct
      Internal Reforming Solid Oxide Fuel Cell.” *International Journal
      of Hydrogen Energy* 37 (3): 2498–2508.
      https://doi.org/10.1016/j.ijhydene.2011.10.051.

   .. container::
      :name: ref-10.1016/j.energy.2009.02.012

      Chakraborty, Uday Kumar. 2009. “Static and Dynamic Modeling of
      Solid Oxide Fuel Cell Using Genetic Programming.” *Energy* 34 (6):
      740–51. https://doi.org/10.1016/j.energy.2009.02.012.

   .. container::
      :name: ref-10.1051/e3sconf/201911302010

      Chen, Jinwei, Yao Chen, and Huisheng Zhang. 2019. “Study on Fuel
      Utilization Dynamic Model of a Sofc-Gt Hybrid System Based on Deep
      Learning Technique.” *E3S Web of Conferences* 113: 02010.
      https://doi.org/10.1051/e3sconf/201911302010.

   .. container::
      :name: ref-10.1016/j.enconman.2017.06.041

      Dolenc, B., P. Boškoski, M. Stepančič, A. Pohjoranta, and Đ.
      Juričić. 2017. “State of Health Estimation and Remaining Useful
      Life Prediction of Solid Oxide Fuel Cell Stack.” *Energy
      Conversion and Management* 148: 993–1002.
      https://doi.org/10.1016/j.enconman.2017.06.041.

   .. container::
      :name: ref-10.1016/j.jpowsour.2007.04.015

      Entchev, Evgueniy, and Libing Yang. 2007. “Application of Adaptive
      Neuro-Fuzzy Inference System Techniques and Artificial Neural
      Networks to Predict Solid Oxide Fuel Cell Performance in
      Residential Microgeneration Installation.” *Journal of Power
      Sources* 170 (1): 122–29.
      https://doi.org/10.1016/j.jpowsour.2007.04.015.

   .. container::
      :name: ref-10.1109/TIE.2008.2009516

      Gebregergis, A., P. Pillay, D. Bhattacharyya, and R. Rengaswemy.
      2008. “Solid Oxide Fuel Cell Modeling.” *IEEE Transactions on
      Industrial Electronics* 56 (1): 139–48.
      https://doi.org/10.1109/tie.2008.2009516.

   .. container::
      :name: ref-10.1016/j.cherd.2012.06.003

      Grondin, D., J. Deseure, P. Ozil, J.-P. Chabriat, B.
      Grondin-Perez, and A. Brisse. 2012. “Solid Oxide Electrolysis Cell
      3D Simulation Using Artificial Neural Network for Cathodic Process
      Description.” *Chemical Engineering Research and Design* 91 (1):
      134–40. https://doi.org/10.1016/j.cherd.2012.06.003.

   .. container::
      :name: ref-10.1016/j.ijhydene.2011.09.148

      GĂźnay, M. Erdem, Fatma Akpinar, Z. Ilsen Onsan, and Ramazan
      Yildirim. 2011. “Investigation of Water Gas-Shift Activity of
      Pt–Mox–Ceo2/Al2o3 (M = K, Ni, Co) Using Modular Artificial Neural
      Networks.” *International Journal of Hydrogen Energy* 37 (3):
      2094–2102. https://doi.org/10.1016/j.ijhydene.2011.09.148.

   .. container::
      :name: ref-10.1016/j.energy.2013.08.031

      Hajimolana, S. A., S. M. Tonekabonimoghadam, M. A. Hussain, M. H.
      Chakrabarti, N. S. Jayakumar, and M. A. Hashim. 2013. “Thermal
      Stress Management of a Solid Oxide Fuel Cell Using Neural Network
      Predictive Control.” *Energy* 62: 320–29.
      https://doi.org/10.1016/j.energy.2013.08.031.

   .. container::
      :name: ref-10.1016/j.ijhydene.2019.09.055

      Han, Jing, Xi Wang, Limei Yan, and Aida Dahlak. 2019. “Modelling
      the Performance of an Soec by Optimization of Neural Network with
      Mpso Algorithm.” *International Journal of Hydrogen Energy* 44
      (51): 27947–57. https://doi.org/10.1016/j.ijhydene.2019.09.055.

   .. container::
      :name: ref-10.3390/pr9020348

      HĂśber, Michael, Benjamin KĂśnigshofer, Philipp Wachter, Gjorgji
      Nusev, Pavle Boskoski, Christoph Hochenauer, and Vanja Subotić.
      2021. “Holistic Approach to Design, Test, and Optimize Stand-Alone
      Sofc-Reformer Systems.” *Processes* 9 (2): 348.
      https://doi.org/10.3390/pr9020348.

   .. container::
      :name: ref-10.1016/j.jpowsour.2008.06.064

      Huo, Hai-Bo, Xin-Jian Zhu, Wan-Qi Hu, Heng-Yong Tu, Jian Li, and
      Jie Yang. 2008. “Nonlinear Model Predictive Control of Sofc Based
      on a Hammerstein Model.” *Journal of Power Sources* 185 (1):
      338–44. https://doi.org/10.1016/j.jpowsour.2008.06.064.

   .. container::
      :name: ref-10.1016/S0378-7753_03_00309-4

      Jurado, Francisco. 2003. “Power Supply Quality Improvement with a
      Sofc Plant by Neural-Network-Based Control.” *Journal of Power
      Sources* 117 (1-2): 75–83.
      https://doi.org/10.1016/s0378-7753(03)00309-4.

   .. container::
      :name: ref-10.1016/j.apenergy.2020.116372

      KĂśnigshofer, Benjamin, Pavle BoĹĄkoski, Gjorgji Nusev, Markus
      Koroschetz, Martin Hochfellner, Marcel Schwaiger,
      :raw-latex:`\DJ`ani Juričić, Christoph Hochenauer, and Vanja
      Subotić. 2021. “Performance Assessment and Evaluation of Soc
      Stacks Designed for Application in a Reversible Operated 150 kW
      rSOC Power Plant.” *Applied Energy* 283: 116372.
      https://doi.org/10.1016/j.apenergy.2020.116372.

   .. container::
      :name: ref-10.1016/j.jpowsour.2021.229875

      KĂśnigshofer, Benjamin, Gernot Pongratz, Gjorgji Nusev, Pavle
      Boškoski, Michael Höber, :raw-latex:`\DJ`ani Juričić, Mihails
      Kusnezoff, et al. 2021. “Development of Test Protocols for Solid
      Oxide Electrolysis Cells Operated Under Accelerated Degradation
      Conditions.” *Journal of Power Sources* 497: 229875.
      https://doi.org/10.1016/j.jpowsour.2021.229875.

   .. container::
      :name: ref-10.1016/j.apenergy.2018.09.092

      Kupecki, Jakub, Davide Papurello, Andrea Lanzini, Yevgeniy
      Naumovich, Konrad Motylinski, Marcin Blesznowski, and Massimo
      Santarelli. 2018. “Numerical Model of Planar Anode Supported Solid
      Oxide Fuel Cell Fed with Fuel Containing H2s Operated in Direct
      Internal Reforming Mode.” *Applied Energy* 230: 1573–84.
      https://doi.org/10.1016/j.apenergy.2018.09.092.

   .. container::
      :name: ref-10.1155/2019/7828019

      Le, Minh-Vien, Tuan-Anh Nguyen, and T.-Anh-Nga Nguyen. 2019.
      “Modeling and Optimization of the Bscf-Based Single-Chamber Solid
      Oxide Fuel Cell by Artificial Neural Network and Genetic
      Algorithm.” *Journal of Chemistry* 2019: 1–9.
      https://doi.org/10.1155/2019/7828019.

   .. container::
      :name: ref-10.1115/1.4003976

      Marchetti, A., A. Gopalakrishnan, B. Chachuat, D. Bonvin, L.
      Tsikonis, A. Nakajo, Z. Wuillemin, and J. Van herle. 2011. “Robust
      Real-Time Optimization of a Solid Oxide Fuel Cell Stack.” *Journal
      of Fuel Cell Science and Technology* 8 (5).
      https://doi.org/10.1115/1.4003976.

   .. container::
      :name: ref-10.1016/j.jpowsour.2013.04.114

      Marra, Dario, Marco Sorrentino, Cesare Pianese, and Boris
      Iwanschitz. 2013. “A Neural Network Estimator of Solid Oxide Fuel
      Cell Performance for on-Field Diagnostics and Prognostics
      Applications.” *Journal of Power Sources* 241: 320–29.
      https://doi.org/10.1016/j.jpowsour.2013.04.114.

   .. container::
      :name: ref-10.1016/j.jpowsour.2017.11.025

      Menzler, Norbert H., Doris Sebold, and Olivier Guillon. 2017.
      “Post-Test Characterization of a Solid Oxide Fuel Cell Stack
      Operated for More Than 30,000 Hours: The Cell.” *Journal of Power
      Sources* 374: 69–76.
      https://doi.org/10.1016/j.jpowsour.2017.11.025.

   .. container::
      :name: ref-10.1016/j.ijhydene.2009.04.068

      Milewski, Jarosław, and Konrad Świrski. 2009. “Modelling the Sofc
      Behaviours by Artificial Neural Network.” *International Journal
      of Hydrogen Energy* 34 (13): 5546–53.
      https://doi.org/10.1016/j.ijhydene.2009.04.068.

   .. container::
      :name: ref-10.1016/j.ijhydene.2013.09.045

      Moçoteguy, Philippe, and Annabelle Brisse. 2013. “A Review and
      Comprehensive Analysis of Degradation Mechanisms of Solid Oxide
      Electrolysis Cells.” *International Journal of Hydrogen Energy* 38
      (36): 15887–15902. https://doi.org/10.1016/j.ijhydene.2013.09.045.

   .. container::
      :name: ref-mutter

      Mütter, Felix. 2021. “Artificial Neural Network Modeling and
      Genetic Algorithm Optimization of Process Parameters of Solid
      Oxide Fuel Cell Systems.” Master’s thesis, Inffeldgasse 25/B, 8010
      Graz, Austria: Graz University of Technology.

   .. container::
      :name: ref-10.1016/j.renene.2019.01.072

      Nassef, Ahmed M., Ahmed Fathy, Enas Taha Sayed, Mohammad Ali
      Abdelkareem, Hegazy Rezk, Waqas Hassan Tanveer, and A. G. Olabi.
      2019. “Maximizing Sofc Performance Through Optimal Parameters
      Identification by Modern Optimization Algorithms.” *Renewable
      Energy* 138: 458–64. https://doi.org/10.1016/j.renene.2019.01.072.

   .. container::
      :name: ref-10.1016/j.jpowsour.2021.229491

      Nusev, Gjorgji, Bertrand Morel, Julie Mougin, :raw-latex:`\DJ`ani
      Juričić, and Pavle Boškoski. 2021. “Condition Monitoring of Solid
      Oxide Fuel Cells by Fast Electrochemical Impedance Spectroscopy: A
      Case Example of Detecting Deficiencies in Fuel Supply.” *Journal
      of Power Sources* 489: 229491.
      https://doi.org/10.1016/j.jpowsour.2021.229491.

   .. container::
      :name: ref-10.1016/j.ijhydene.2016.06.143

      Pahon, E., N. Yousfi Steiner, S. Jemei, D. Hissel, M. C. PĂŠra, K.
      Wang, and P. Moçoteguy. 2016. “Solid Oxide Fuel Cell Fault
      Diagnosis and Ageing Estimation Based on Wavelet Transform
      Approach.” *International Journal of Hydrogen Energy* 41 (31):
      13678–87. https://doi.org/10.1016/j.ijhydene.2016.06.143.

   .. container::
      :name: ref-10.1007/s40095-018-0269-5

      Salehi, Zahra, and Iman Gholaminezhad. 2018. “Multi-Objective
      Modeling, Uncertainty Analysis, and Optimization of Reversible
      Solid Oxide Cells.” *International Journal of Energy and
      Environmental Engineering* 9 (3): 295–304.
      https://doi.org/10.1007/s40095-018-0269-5.

   .. container::
      :name: ref-10.3390/en13071621

      Song, Changhee, Sanghoon Lee, Bonhyun Gu, Ikwhang Chang, Gu Young
      Cho, Jong Dae Baek, and Suk Won Cha. 2020. “A Study of
      Anode-Supported Solid Oxide Fuel Cell Modeling and Optimization
      Using Neural Network and Multi-Armed Bandit Algorithm.” *Energies*
      13 (7): 1621. https://doi.org/10.3390/en13071621.

   .. container::
      :name: ref-10.1016/j.ijhydene.2021.03.132

      Song, Shaohui, Xingyu Xiong, Xin Wu, and Zhenzhong Xue. 2021.
      “Modeling the Sofc by Bp Neural Network Algorithm.” *International
      Journal of Hydrogen Energy* 46 (38): 20065–77.
      https://doi.org/10.1016/j.ijhydene.2021.03.132.

   .. container::
      :name: ref-10.1016/j.egypro.2014.01.032

      Sorrentino, M., D. Marra, C. Pianese, M. Guida, F. Postiglione, K.
      Wang, and A. Pohjoranta. 2014. “On the Use of Neural Networks and
      Statistical Tools for Nonlinear Modeling and on-Field Diagnosis of
      Solid Oxide Fuel Cell Stacks.” *Energy Procedia* 45: 298–307.
      https://doi.org/10.1016/j.egypro.2014.01.032.

   .. container::
      :name: ref-SUBOTIC2021113764

      Subotić, Vanja, Michael Eibl, and Christoph Hochenauer. 2021.
      “Artificial Intelligence for Time-Efficient Prediction and
      Optimization of Solid Oxide Fuel Cell Performances.” *Energy
      Conversion and Management* 230: 113764.
      https://doi.org/https://doi.org/10.1016/j.enconman.2020.113764.

   .. container::
      :name: ref-10.1039/D0SE01914C

      Subotić, Vanja, Philipp Harter, Mihails Kusnezoff, Teko W.
      Napporn, Hartmuth Schroettner, and Christoph Hochenauer. 2021.
      “Identification of Carbon Deposition and Its Removal in Solid
      Oxide Fuel Cells by Applying a Non-Conventional Diagnostic Tool.”
      *Sustainable Energy & Fuels* 5 (7): 2065–76.
      https://doi.org/10.1039/d0se01914c.

   .. container::
      :name: ref-10.1016/j.apenergy.2020.115603

      Subotić, Vanja, Norbert H. Menzler, Vincent Lawlor, Qingping Fang,
      Stefan Pofahl, Philipp Harter, Hartmuth Schroettner, and Christoph
      Hochenauer. 2020. “On the Origin of Degradation in Fuel Cells and
      Its Fast Identification by Applying Unconventional
      Online-Monitoring Tools.” *Applied Energy* 277: 115603.
      https://doi.org/10.1016/j.apenergy.2020.115603.

   .. container::
      :name: ref-10.1016/j.ijhydene.2020.07.165

      Subotić, Vanja, Thomas Thaller, Benjamin Königshofer, Norbert H.
      Menzler, Edith Bucher, Andreas Egger, and Christoph Hochenauer.
      2020. “Performance Assessment of Industrial-Sized Solid Oxide
      Cells Operated in a Reversible Mode: Detailed Numerical and
      Experimental Study.” *International Journal of Hydrogen Energy* 45
      (53): 29166–85. https://doi.org/10.1016/j.ijhydene.2020.07.165.

   .. container::
      :name: ref-10.1016/j.jpowsour.2012.09.061

      Tietz, F., D. Sebold, A. Brisse, and J. Schefold. 2012.
      “Degradation Phenomena in a Solid Oxide Electrolysis Cell After
      9000 H of Operation.” *Journal of Power Sources* 223: 129–35.
      https://doi.org/10.1016/j.jpowsour.2012.09.061.

   .. container::
      :name: ref-10.1016/j.jpowsour.2016.04.080

      Wu, XiaoJuan, and Qianwen Ye. 2016. “Fault Diagnosis and
      Prognostic of Solid Oxide Fuel Cells.” *Journal of Power Sources*
      321: 47–56. https://doi.org/10.1016/j.jpowsour.2016.04.080.

   .. container::
      :name: ref-10.1631/jzus.2007.A1505

      Wu, Xiao-juan, Xin-jian Zhu, Guang-yi Cao, and Heng-yong Tu. 2007.
      “Nonlinear Modelling of a Sofc Stack by Improved Neural Networks
      Identification.” *Journal of Zhejiang University-SCIENCE A* 8 (9):
      1505–9. https://doi.org/10.1631/jzus.2007.a1505.

   .. container::
      :name: ref-10.1016/j.jpowsour.2007.12.036

      Wu, Xiao-Juan, Xin-Jian Zhu, Guang-Yi Cao, and Heng-Yong Tu. 2007.
      “Predictive Control of Sofc Based on a Ga-Rbf Neural Network
      Model.” *Journal of Power Sources* 179 (1): 232–39.
      https://doi.org/10.1016/j.jpowsour.2007.12.036.

   .. container::
      :name: ref-10.1016/j.egyai.2020.100003

      Xu, Haoran, Jingbo Ma, Peng Tan, Bin Chen, Zhen Wu, Yanxiang
      Zhang, Huizhi Wang, Jin Xuan, and Meng Ni. 2020. “Towards Online
      Optimisation of Solid Oxide Fuel Cell Performance: Combining Deep
      Learning with Multi-Physics Simulation.” *Energy and AI* 1:
      100003. https://doi.org/10.1016/j.egyai.2020.100003.

   .. container::
      :name: ref-10.1016/j.electacta.2017.11.180

      Yan, Y., Q. Fang, L. Blum, and W. Lehnert. 2017. “Performance and
      Degradation of an Soec Stack with Different Cell Components.”
      *Electrochimica Acta* 258: 1254–61.
      https://doi.org/10.1016/j.electacta.2017.11.180.

   .. container::
      :name: ref-10.1016/j.enconman.2019.111916

      Yan, Z., A. He, S. Hara, and N. Shikazono. 2019. “Modeling of
      Solid Oxide Fuel Cell (Sofc) Electrodes from Fabrication to
      Operation: Microstructure Optimization via Artificial Neural
      Networks and Multi-Objective Genetic Algorithms.” *Energy
      Conversion and Management* 198: 111916.
      https://doi.org/10.1016/j.enconman.2019.111916.

   .. container::
      :name: ref-10.1016/j.ijhydene.2015.04.042

      Zahadat, Pouya, and Jaroslaw Milewski. 2015. “Modeling Electrical
      Behavior of Solid Oxide Electrolyzer Cells by Using Artificial
      Neural Network.” *International Journal of Hydrogen Energy* 40
      (23): 7246–51. https://doi.org/10.1016/j.ijhydene.2015.04.042.

   .. container::
      :name: ref-10.1016/j.electacta.2017.08.113

      Zhang, Caizhi, Qinglin Liu, Qi Wu, Yifeng Zheng, Juan Zhou,
      Zhengkai Tu, and Siew Hwa Chan. 2017. “Modelling of Solid Oxide
      Electrolyser Cell Using Extreme Learning Machine.” *Electrochimica
      Acta* 251: 137–44.
      https://doi.org/10.1016/j.electacta.2017.08.113.

   .. container::
      :name: ref-10.1016/j.apenergy.2018.10.113

      Zhang, Zehan, Shuanghong Li, Yawen Xiao, and Yupu Yang. 2018.
      “Intelligent Simultaneous Fault Diagnosis for Solid Oxide Fuel
      Cell System Based on Deep Learning.” *Applied Energy* 233-234:
      930–42. https://doi.org/10.1016/j.apenergy.2018.10.113.

   .. container::
      :name: ref-10.1016/j.apenergy.2021.117101

      Žnidarič, Luka, Gjorgji Nusev, Bertrand Morel, Julie Mougin,
      :raw-latex:`\DJ`ani Juričić, and Pavle Boškoski. 2021. “Evaluating
      Uncertainties in Electrochemical Impedance Spectra of Solid Oxide
      Fuel Cells.” *Applied Energy* 298: 117101.
      https://doi.org/10.1016/j.apenergy.2021.117101.

   .. container::
      :name: ref-10.1109/tcst.2015.2502899

      Zou, Changfu, Chris Manzie, and Dragan Nesic. 2015. “A Framework
      for Simplification of Pde-Based Lithium-Ion Battery Models.” *IEEE
      Transactions on Control Systems Technology* 24 (5): 1594–1609.
      https://doi.org/10.1109/tcst.2015.2502899.